Extreme Value Theory: Limiting Distributions and Applications

This lecture covers Extreme Value Theory, focusing on the limiting distribution of normalized maxima, GEV distribution, block-maxima method, GPD, and threshold exceedances. It explains the concepts of maxima, limiting distributions of sums, and the Fisher-Tippett-Gnedenko Theorem. The lecture also delves into Generalized Extreme Value (GEV) Distributions, GEV distribution functions, and GEV density functions. Additionally, it discusses the Fréchet and Gumbel cases, the Pickands-Balkema-de Haan Theorem, and the modelling of excess losses using the GPD. The lecture concludes with topics like the sample mean excess plot, threshold selection trade-off, and estimated tail distribution.